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This chapter starts by presenting Hempel's account of statistical explanation. Hempel proposed to deal with the problem of epistemic ambiguity in statistical explanation by a requirement of maximal specificity in the reference-class. But, as Salmon has shown, the reference-class needs to be narrowed only in statistically relevant ways. Also, it needs to be homogeneous. In effect, both requirements seek to maximize inductive probability. So, successful statistical explanations do not need to invoke high statistical probabilities, but favourably relevant ones that have high inductive...

This chapter starts by presenting Hempel's account of statistical explanation. Hempel proposed to deal with the problem of epistemic ambiguity in statistical explanation by a requirement of maximal specificity in the reference-class. But, as Salmon has shown, the reference-class needs to be narrowed only in statistically relevant ways. Also, it needs to be homogeneous. In effect, both requirements seek to maximize inductive probability. So, successful statistical explanations do not need to invoke high statistical probabilities, but favourably relevant ones that have high inductive probability. Additionally, Salmon's arguments for saying that even favourable relevance is unnecessary rest on a failure to distinguish between explanations how a certain event was possible and explanations why it occurred. Finally, the mathematical probabilities involved in statistical explanation are not amenable to interpretation as relative frequencies, and must be given a propensity interpretation.